M03 controller described multiple separation events that involved takeover situations as the aircraft were slowing at 10;000; the reporter claiming ZME frequently fails to provide adequate separation.

Narrative

I was working West Arrival and had accepted hand-offs on Aircraft A and Aircraft B; both medium large transports (MLT) on the UJM3 Arrival from the Southwest. As Aircraft A leveled at 10;000 FT; they slowed to 300 KTS indicated. Aircraft B was descending out at 11;000 and Memphis Center (ZME) was vectoring them to maintain spacing behind Aircraft A still indicating 380 KTS. When I first talked to Aircraft B; they were leveling at 10;000 FT and indicating 340 KTS. They said they were slowing to 250 KTS. I instructed them to slow to 210 KTS. I had already descending Aircraft A to 6000 FT with an expedited descent through 9000 FT when that aircraft had entered my airspace. I immediately advised ZME that I was slowing Aircraft B in their airspace to maintain wake turbulence separation; and ZME gave me control. Later; while working the same position; I accepted hand-offs on Aircraft C (MLT) and Aircraft D. both aircraft on the UJM3 Arrival descending to 10;000 FT. Aircraft C reduced speed to 300 KTS at 10;000 FT. Aircraft D was still indicating 400 KTS as they descended out of 13;000 FT about 9 miles in trail. When I talked to Aircraft D; I told them to slow to 210 KTS and then maintain 10;000 FT. I requested approval from ZME for these actions in their airspace and was given control. I also had to issue and expedited descent clearance to Aircraft C to maintain wake turbulence separation. Seven minutes later I was working Aircraft E and Aircraft F (both MLTs); inbound on the UJM3 Arrival. Again; Aircraft E; the lead aircraft; slowed to 300 KTS (I should mention that this was what 250 KTS true airspeed indicated) while Aircraft F continued at about 380 KTS indicated. This time; when Aircraft F leveled at 10;000 FT; the aircraft also slowed to 300 KTS indicated in time to avoid being a factor for Aircraft E's wake. I had already filed a report on an earlier event from today; so this makes four times that it has happened just this morning. I hope that companies involved; ZME; or both will take action.